UCLA Student Body President Michael Skiles identified Professor William S. Klug as the individual who was slain.
Klug is a professor of mechanical and aerospace engineering, according to the UCLA's website. He received his undergraduate degree at Westmont College, then obtained a Masters at UCLA and a Ph.D. Caltech.
He also led the Klug Research Group, which studied "problems at the interface of mechanics and biology."
"We aim to understand how the physical properties of biological structures and materials are involved in biological function from molecular and cellular scales upward," the group's website says.
The situation was contained by shortly after noon, and there was no ongoing threat to to the campus, Los Angeles Police Chief Charlie Beck said. He said police found a weapon, and no suspects remain at large.
UCLA said classes were canceled for the rest of Wednesday, but are expected to resume Thursday, except for the engineering school, where the death occurred. Classes there will resume Monday, officials said.
Beck said the shooting took place in a small office in the engineering building. He said he did not know whether the dead were students.
Authorities had received reports of an active shooter in or near the building, Los Angeles Police Officer Tony Im said.
Officials put the campus on lockdown as authorities investigated. Throngs of police with long guns patrolled the streets of the campus of more than 40,000 students.
SWAT officers and dozens of squad cars filled the area as police tried to clear campus buildings floor by floor.
Freshman Teddi Mattox said she was in a cafeteria getting breakfast with about 100 other students when the shooting occurred.
"We got the alert and a woman said, 'This is not a joke, everyone get to the back of the dining hall because we have to stay away from the windows,'" she said.
"We're crowded back here, we've been here for at least an hour and a half. People are crying, they're nervous, they're shaking ... I have not stopped shaking for the last hour and a half."
UCLA officials said they will review all campus safety procedures.
"We're pleased in the way notification went out, troubled by some reports of unlocked doors, but we want to review everything," said Scott Waugh, UCLA's executive vice chancellor and provost.
UCLA has also extended counseling services over the next few days to serve all the students who may be in need, Waugh said.
Los Angeles police is still investigating the shooting, according to university officials.
Police urged residents to avoid the UCLA campus.
CNN law enforcement analyst Tom Fuentes said locking down a large university in an urban area is a "monumental task." UCLA's engineering building is in the middle of a very densely populated part of Los Angeles.
UCLA's final exams are scheduled for next week, with graduation set for Friday.
The engineering school's senior class dinner was scheduled for Thursday night.
According to UCLA, the school is known as the "birthplace of the Internet" because in 1969, the first transmission on what would become the Internet was sent from the engineering school's Boelter Hall.